Saturday, March 06, 2010

UPDATE: Turns out that Beenstock and Reingewertz Beenstock et al were clueless about the data they used.
In particular, point out that the greenhouse gas
concentrations they used was not a single series but changes from ice cores in 1960 to atmospheric
grab samples. This throws B&Rs analysis into the trash can. See here for details

UPDATE: Could somebunny point Eli to a consistent set of forcings in numerical format going back to the year dot.

So the new best thing in the denialsphere is a paper by Michael Beenstock and Yaniv Reingewertz from the Department of Economics of the The Hebrew University where they pull a Wegman, analyzing climate data without knowing anything about the science. Now this is par for the course in economics where there are no constraints, but it ain't so cool when you deal with physical reality. Anyhow, the rubber hits the road very quickly when they say that

The method of co-integration is designed to test hypotheses with time series data that are non-stationary to the same order, and to avoid the pitfall of spurious regression. The order of non-stationarity refers to the number of times a variable must be differenced (d) to render it stationary, in which case the variable is integrated of order, d, or I(d). We confirm previous findings, that the radiative forcings of greenhouse gases (C02, CH4 and N2O) are stationary in second differences (i.e. I(2)) while global temperature and solar irradiance are stationary in first differences (i.e. I(1)).

Straightforwardly this is a claim that forcing has been increasing as a second order function, while temperature has only been increasing linearly. Given the noise in the temperature record, that is a reach as an absolute, but Eli is a nice Rabett. Still, as one of the mice said, whoa. The best estimates of the radiative forcing is the NOAA Annual Greenhouse Gas Index, which was first described in a paper by Hofmann, et al. and considers all forcings since 1979. Why 1979? Well that's when they established the NOAA Earth System Research Laboratory global cooperative air sampling network. It's also the year when Eli got a tenure track job. Makes sense.

If you look at the CO2 forcing above it looks pretty linear, but how about the total radiative forcing, because, our new hero's are claiming that

.......greenhouse gas forcing, global temperature and solar irradiance are not polynomially cointegrated and AGW is refuted. Although we reject AGW, we find that greenhouse gas forcings have a temporary effect on global temperature. Because the greenhouse effect is temporary rather than permanent, predicitons of significant global warming in the 21st century by IPCC are not supported by the data.

Hmm, that looks pretty linear too (the color you can't see in the legend is for CH4). So we have the result that the radiative forcing since 1979, has been linear. What about before 1979? Well, let's go to the IPCC WGI. Calculation of radiative forcing requires calculations, that means models. The figure below is from Nozawa et al., 2005; and Takemura et al., 2005. Different GCMs, get different values, but the general trends are as shown. Even if you simply plug into simple algebraic equations to calculate the radiative forcings, those equations came from GCMs, so in a real sense Beenstock and Reingewertz are unwittingly engaging in a circle jerk, but let the magnomious Rabett Labs skip over this,The bunnies tossed back a few beers, took out the ruler and said, hey, that total forcing looks a lot more like two straight lines with a hinge than a second order curve, and indeed, to be fair, the same thought had occurred to B&R

We also check whether rfCO2 is I(1) subject to a structural break. A break in the stochastic trend of rfCO2 might create the impression that d = 2 when in fact its true value is 1. We apply the test suggested by Clemente, Montanas and Reyes (1998) (CMR).xvi The CMR statistic (which is the ADF statistic allowing for a break) for the first difference of rfCO2 is -3.877. The break occurs in 1964, but since the critical value of the CMR statistic is -4.27 we can safely reject the hypothesis that rfCO2 is I(1) with a break in its stochastic trend.

BUT, the period they looked at was 1880 - 2000. Zeroth order dicking around says that any such test between a second order dependence and two hinged lines is going to be affected strongly by the length of the record. Any bunnies wanna bet what happens if you use a longer record???

You really can't tell, they reference radiative forcing and at least formally appear to consider methane, nitrous oxide and solar irradiance, but there is no real reference which allows you to figure out where the radiative forcing numbers came from. Eli suspects their ref 14 points to the wrong paper from GISS but should point to one that has forcings.

I'm not getting how this is at all a sensible thing to do. If you "difference" GHG forcings twice you definitely don't get something "stationary" in the sense of constant. Is there something else I'm missing? GHG forcings are non-polynomial in time, as are all the others, as is the temperature response. Polynomial fits might make sense over short periods of time while changes are roughly linear, or running through a maximum (since almost every max/min is quadratic). But we don't have either of those here...

"If you "difference" GHG forcings twice you definitely don't get something "stationary" in the sense of constant."

It isn't constant, it's uncorrelated noise with a mean of zero, which is stationary by definition in time series analysis.

An I(0) process does not have a unit root. An I(1) process has a unit root. The first difference of an I(2) process has a unit root. Having a unit root is identical to having an AR(1) noise distribution or a lag-1 autocorrelation coefficient of 1. That means point y(t) = y(t-1) + Z where Z is not a constant but white noise of mean zero. An I(1) process is, in ARIMA (Autoregressive, integrated, moving average) nomenclature a (0,1,0) process. Life gets complicated, though because an AR process with a near unit lag-1 coefficient may not be distinguishable from an I(1) process depending on the level of noise.

I constructed a simple conceptual model based on decades, with a lag of one decade in applyiung the CO2 forcing. CO2 alone accounts for 96% of the observed variance. Using about (1/3) of the AMO for internal variability and minor forcings accounts for another 3% of the variance. Details here.

Think of this as a simplified version of Tamino's two box model plus the AMO.

IPCC AR4 WG1 has fairly strong cautionary language regarding at least volcanic aerosol forcings. Gavin Schmidt has repeatedly pointed out in comments on RealClimate that adding up all the forcings, at least the way GISS does it for ModelE, results in a net forcing about equal to that of CO2 alone. This pdf paper has some cautionary language regarding TSI, but still concldues that GHGs account for 90% of the variance.

David Benson - many thanks for that link to Judith Lean's latest, but her claim that 'anthropogenic effects account for 90% of industrial global warming' is absurd. Her total solar irradiance (TSI) is the output from the sun, while the surface solar radiation (SSR) is what reaches individual locations on the surface of the globe and is by no means to be equated with TSI, which barely changes, whereas SSR varies enormously. Using NOAA data, I find that the RF of CO2 as the chief GHG is NEVER a stat. sig. determinant of changes in temperature at any given location in the USA, unlike changes in SSR. Thus my findings complement those of Beenstock, and rebut Lean.

Tim Curtin is insiring a comment:"while the surface solar radiation (SSR) is what reaches individual locations on the surface of the globe and is by no means to be equated with TSI, which barely changes, whereas SSR varies enormously."

Because if TSI was the same as SSR, we could send a rocket ship to the sun at night! Curtin's "analysis" is equally profound analysis, I am sure.

Before others spend too much effort on this, the authors should check the reliability of their approach by applying it to model data on global temperature trends with and without anthropogenic forcings. Clearly, if their method does not find the effect of CO2 forcing in model outputs that explicitly include it, the method has a problem.

Tracy obviously belongs to the Kiehl-Trenberth school of flat earth and permanent daylight school of climatologists (enshrined in the IPCC's AR4). Amazingly enough perhaps for Tracy, temperatures at Pt Barrow in Alaska are not quite the same as in LA or NYC, even though the atmospheric CO2 is, but not the SSR. It is indeed odd how climatologists like Lean and Tracy focus on the sun's output at ToA and [CO2] but ignore all other climatic variables, such as SSR and RH.

To elaborate on DeWitt, an l(0) process is white noise and an l(1) process, a classical random walk ("brownian motion"). l(2) is a bit harder to describe: perhaps the location of a vehicle tracked by an inertial device, where the acceleration is "noisy".

It is clear to me that the nonsense assumption that shoots down this B&R thing is the lack of any constraint, nicely hidden in the stats talk, on the possible magnitude of natural unforced variability in temperature. Yes, it is trivially true that if you allow for a large enough natural variability, you cannot rule out with any confidence that it is that which has produced the temperature upswing since 1980.

The question to ask, which B&R conspicuously do not, is, how physically realistic that is.

As the Wabett sayz:

Now this is par for the course in economics where there are no constraints, but it ain't so cool when you deal with physical reality.

DeWitt - but the second derivative (or "difference") of CO2 concentration is most definitely not "uncorrelated noise with a mean of zero". It is not "noise" at all, it's entirely traceable to human fossil fuel consumption, which has a specific growth pattern that is close to exponential (with oil-shock and economic-collapse variations). And an exponential curve has positive n'th "differences" for every value of n!

Arthur said:"And an exponential curve has positive n'th "differences" for every value of n!"

But if you take the second difference of the actual data, there's enough noise that, while it fails a normality test, the lag-1 correlation coefficient is small enough that it fails the unit root test. In terms of cointegration, if the second difference had a unit root, then it would be I(3) or higher and it would be even worse. But the whole thing is bogus, IMO, in that the test was designed for variables that were not known to be related to see if a correlation between them was spurious. There is a known mechanism between ghg's and temperature so whether it passes the test or not is irrelevant. But I'm not an expert on cointegration so it's just my opinion.

DeWitt - well, I think Eli's point was the only reason they are seeing I(2) is because they include a particular time interval. For a few decades, it's linear (I(1) presumably). Go back 2000 years, or 600,000 years on CO2 and see how it works...

Arthur - Yes, I agree. I'm sure that if you plugged the Vostok CO2 and temperature record into the meat grinder, they would be of the same integration order, probably I(1), and would be highly correlated, especially if one used a model with a time constant and/or lag. I'd do it, but I think the time series need to be simultaneous and have constant size time intervals. I don't know how, other than brute force interpolation which is too labor intensive, to do that. Probably somebody, somewhere, has already done it.

“the GHG forcings are l(2) and temperatures are l(1) so they cannot be cointegrated, as this makes them asymptotically independent.”

Let me see. I take a diode, biased in the exponential region, and put a varying current through it. I measure both the current and the voltage drop across the diode and discover that I is exponential and V is linear, therefore they are “asymptotically independent”

"GLOBAL warming is set to become global cooling this century, a leading analyst claimed yesterday. Professor Michael Beenstock said theories of climate change are wrong. He warned climatologists have misused statistics, leading them to the mistaken conclusion global warming is evidence of the greenhouse effect. He told London’s Cass Business School that the link between rising greenhouse gas emissions and rising temperatures is “spurious”, adding: “The greenhouse effect is an illusion.”"

The moron doesn't even understand that the "evidence" of the greenhouse effect is measurements of the spectroscopic properties of gases. Please squash like a bug.

I'm now convinced that the data B&R used for the forcings is not raw data. It's been smoothed or otherwise manipulated. I took the Mauna Loa annual CO2 data from 1958-2009, calculated the log ratio and tested that with the augmented Dewey-Fuller test for unit root. It's I(1), not I(2). The ghg column in the GISS file I linked above for about the same time period, OTOH, is still I(2). Boom, your battleship has been sunk.

Thanks for this post, I hope that I can visit your blog every day but unfortunately I can't do that. By the way, can you have a review about google +1 effect? I just want to know it better. Thanks again! :)

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Eli Rabett

Eli Rabett, a not quite failed professorial techno-bunny who finally handed in the keys and retired from his wanna be research university. The students continue to be naive but great people and the administrators continue to vary day-to-day between homicidal and delusional without Eli's help. Eli notices from recent political developments that this behavior is not limited to administrators. His colleagues retain their curious inability to see the holes that they dig for themselves. Prof. Rabett is thankful that they, or at least some of them occasionally heeded his pointing out the implications of the various enthusiasms that rattle around the department and school. Ms. Rabett is thankful that Prof. Rabett occasionally heeds her pointing out that he is nuts.